Analysis of Separable Markov-Modulated Rate Models for Information-Handling Systems

@article{citeulike:2737562, abstract = {In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP). In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the 'state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique.}, author = {Stern, Thomas E. and Elwalid, Anwar I. }, citeulike-article-id = {2737562}, doi = {10.2307/1427514}, journal = {Advances in Applied Probability}, keywords = {test}, number = {1}, pages = {105--139}, posted-at = {2008-04-30 12:11:06}, priority = {2}, publisher = {Applied Probability Trust}, title = {Analysis of Separable Markov-Modulated Rate Models for Information-Handling Systems}, url = {http://dx.doi.org/10.2307/1427514}, volume = {23}, year = {1991} }

TY - JOUR ID - citeulike:2737562 L3 - citeulike-article-id:2737562 TI - Analysis of Separable Markov-Modulated Rate Models for Information-Handling Systems JF - Advances in Applied Probability VL - 23 IS - 1 SP - 105 EP - 139 PB - Applied Probability Trust N2 - In many communication and computer systems, information arrives to a multiplexer, switch or information processor at a rate which fluctuates randomly, often with a high degree of correlation in time. The information is buffered for service (the server typically being a communication channel or processing unit) and the service rate may also vary randomly. Accurate capture of the statistical properties of these fluctuations is facilitated by modeling the arrival and service rates as superpositions of a number of independent finite state reversible Markov processes. We call such models separable Markov-modulated rate processes (MMRP). In this work a general mathematical model for separable MMRPs is presented, focusing on Markov-modulated continuous flow models. An efficient procedure for analyzing their performance is derived. It is shown that the 'state explosion' problem typical of systems composed of a large number of subsystems, can be circumvented because of the separability property, which permits a decomposition of the equations for the equilibrium probabilities of these systems. The decomposition technique (generalizing a method proposed by Kosten) leads to a solution of the equilibrium equations expressed as a sum of terms in Kronecker product form. A key consequence of decomposition is that the computational complexity of the problem is vastly reduced for large systems. Examples are presented to illustrate the power of the solution technique. KW - test AU - Stern, Thomas AU - Elwalid, Anwar PY - 1991/// UR - http://dx.doi.org/10.2307/1427514 ER -